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Lhprobe

Lhprobe->signedp

Get the signedp field from a lhprobe.

Signature
(lhprobe->signedp x) → signedp
Arguments: x — Guard (lhprobe-p x).
Returns: signedp — Type (booleanp signedp).

This is an ordinary field accessor created by defprod.

Definitions and Theorems

Function: lhprobe->signedp$inline

(defun lhprobe->signedp$inline (x)
  (declare (xargs :guard (lhprobe-p x)))
  (declare (xargs :guard t))
  (let ((__function__ 'lhprobe->signedp))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((x (and t x)))
           (bool-fix (cdr (cdr x))))
         :exec (cdr (cdr x)))))

Theorem: booleanp-of-lhprobe->signedp

(defthm booleanp-of-lhprobe->signedp
  (b* ((signedp (lhprobe->signedp$inline x)))
    (booleanp signedp))
  :rule-classes :type-prescription)

Theorem: lhprobe->signedp$inline-of-lhprobe-fix-x

(defthm lhprobe->signedp$inline-of-lhprobe-fix-x
  (equal (lhprobe->signedp$inline (lhprobe-fix x))
         (lhprobe->signedp$inline x)))

Theorem: lhprobe->signedp$inline-lhprobe-equiv-congruence-on-x

(defthm lhprobe->signedp$inline-lhprobe-equiv-congruence-on-x
  (implies (lhprobe-equiv x x-equiv)
           (equal (lhprobe->signedp$inline x)
                  (lhprobe->signedp$inline x-equiv)))
  :rule-classes :congruence)